We present a microscopic model of granular medium to study the role of dynamical correlations and the onset of spatial order induced by the inelasticity of the interactions on the velocity field. In spite of its simplicity and intrinsic limitations, it feature's several aspects of the rich phenomenology observed in granular materials and allows to make contact with other topics of statistical mechanics such as diffusion processes, domain growth, aging phenomena. Interestingly, while local observables, being controlled by the largest wavelength fluctuations, seem to suggest a purely diffusive behavior, the formation of spatially extended structures, and topological defects, such as vortices and shocks, reveals a more complex scenario. Finally, only for quasielastic systems, we observe a neat scale separation, which represents a fundamental hypothesis to develop a granular hydrodynamics.

We present a microscopic model of granular medium to study the role of dynamical correlations and the onset of spatial order induced by the inelasticity of the interactions on the velocity field. In spite of its simplicity and intrinsic limitations, it feature's several aspects of the rich phenomenology observed in granular materials and allows to make contact with other topics of statistical mechanics such as diffusion processes, domain growth, aging phenomena. Interestingly, while local observables, being controlled by the largest wavelength fluctuations, seem to suggest a purely diffusive behavior, the formation of spatially extended structures, and topological defects, such as vortices and shocks, reveals a more complex scenario. Finally, only for quasielastic systems, we observe a neat scale separation, which represents a fundamental hypothesis to develop a granular hydrodynamics.